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<div class="title">jama_cholesky.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#ifndef JAMA_CHOLESKY_H</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#define JAMA_CHOLESKY_H</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#include &quot;math.h&quot;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;        <span class="comment">/* needed for sqrt() below. */</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;</div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;</div>
<div class="line"><a name="l00008"></a><span class="lineno"><a class="code" href="namespace_j_a_m_a.html">    8</a></span>&#160;<span class="keyword">namespace </span>JAMA</div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;{</div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;</div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="keyword">using namespace </span>TNT;</div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> Real&gt;</div>
<div class="line"><a name="l00047"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_cholesky.html">   47</a></span>&#160;<span class="keyword">class </span><a class="code" href="class_j_a_m_a_1_1_cholesky.html">Cholesky</a></div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;{</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;        <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> L_;               <span class="comment">// lower triangular factor</span></div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;        <span class="keywordtype">int</span> isspd;                              <span class="comment">// 1 if matrix to be factored was SPD</span></div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;<span class="keyword">public</span>:</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;        <a class="code" href="class_j_a_m_a_1_1_cholesky.html">Cholesky</a>();</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;        <a class="code" href="class_j_a_m_a_1_1_cholesky.html">Cholesky</a>(<span class="keyword">const</span> <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> &amp;A);</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;        <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> getL() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;        <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a> solve(<span class="keyword">const</span> <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a> &amp;B);</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;        <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> solve(<span class="keyword">const</span> <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> &amp;B);</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        <span class="keywordtype">int</span> is_spd() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;};</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> Real&gt;</div>
<div class="line"><a name="l00064"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_cholesky.html#a0af68661b83b7a6be938b42e2b2591b6">   64</a></span>&#160;<a class="code" href="class_j_a_m_a_1_1_cholesky.html">Cholesky&lt;Real&gt;::Cholesky</a>() : L_(0,0), isspd(0) {}</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> Real&gt;</div>
<div class="line"><a name="l00071"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_cholesky.html#ab8ac7d6f0c9ef4e0fb74b001fe03ff90">   71</a></span>&#160;<span class="keywordtype">int</span> <a class="code" href="class_j_a_m_a_1_1_cholesky.html#ab8ac7d6f0c9ef4e0fb74b001fe03ff90">Cholesky&lt;Real&gt;::is_spd</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;        <span class="keywordflow">return</span> isspd;</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;}</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> Real&gt;</div>
<div class="line"><a name="l00080"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_cholesky.html#a274b8bbd584bcf84ec860a24aa2b8b2a">   80</a></span>&#160;<a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> <a class="code" href="class_j_a_m_a_1_1_cholesky.html#a274b8bbd584bcf84ec860a24aa2b8b2a">Cholesky&lt;Real&gt;::getL</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;        <span class="keywordflow">return</span> L_;</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;}</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> Real&gt;</div>
<div class="line"><a name="l00092"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_cholesky.html#af859c41220c4313470d28fa13706ff63">   92</a></span>&#160;<a class="code" href="class_j_a_m_a_1_1_cholesky.html#a0af68661b83b7a6be938b42e2b2591b6">Cholesky&lt;Real&gt;::Cholesky</a>(<span class="keyword">const</span> <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> &amp;A)</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;{</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;        <span class="keywordtype">int</span> m = A.<a class="code" href="class_t_n_t_1_1_array2_d.html#a3997cd7973cd903cc46c0bd7abde03c0">dim1</a>();</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;        <span class="keywordtype">int</span> n = A.<a class="code" href="class_t_n_t_1_1_array2_d.html#a6efd5ac98f02bb42340be1d5cbf4c9c1">dim2</a>();</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;        </div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;        isspd = (m == n);</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;        <span class="keywordflow">if</span> (m != n)</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;        {</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;                L_ = <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a>(0,0);</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;                <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;        }</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;        L_ = <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a>(n,n);</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;      <span class="comment">// Main loop.</span></div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;     <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) </div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;         {</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;        Real d(0.0);</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; j; k++) </div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;                {</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;            Real s(0.0);</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; k; i++) </div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;                        {</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;               s += L_[k][i]*L_[j][i];</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;            }</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;            L_[j][k] = s = (A[j][k] - s)/L_[k][k];</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;            d = d + s*s;</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;            isspd = isspd &amp;&amp; (A[k][j] == A[j][k]); </div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;         }</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;         d = A[j][j] - d;</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;         isspd = isspd &amp;&amp; (d &gt; 0.0);</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;         L_[j][j] = sqrt(d &gt; 0.0 ? d : 0.0);</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = j+1; k &lt; n; k++) </div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;                 {</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;            L_[j][k] = 0.0;</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;         }</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;        }</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;}</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> Real&gt;</div>
<div class="line"><a name="l00146"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_cholesky.html#af0f727e2b0e989f7606cdb49de69f119">  146</a></span>&#160;<a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a> <a class="code" href="class_j_a_m_a_1_1_cholesky.html#af0f727e2b0e989f7606cdb49de69f119">Cholesky&lt;Real&gt;::solve</a>(<span class="keyword">const</span> <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a> &amp;b)</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;{</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;        <span class="keywordtype">int</span> n = L_.<a class="code" href="class_t_n_t_1_1_array1_d.html#ad0e3ae296c57454d4244f44076cd1e02">dim1</a>();</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;        <span class="keywordflow">if</span> (b.<a class="code" href="class_t_n_t_1_1_array1_d.html#ad0e3ae296c57454d4244f44076cd1e02">dim1</a>() != n)</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;                <span class="keywordflow">return</span> <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a>();</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;        <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a> x = b.<a class="code" href="class_t_n_t_1_1_array1_d.html#a6b9314ad3f1b8781c56447501a36809d">copy</a>();</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;      <span class="comment">// Solve L*y = b;</span></div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; n; k++) </div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;          {</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; k; i++) </div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;               x[k] -= x[i]*L_[k][i];</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;                 x[k] /= L_[k][k];</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;                </div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;      }</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;      <span class="comment">// Solve L&#39;*X = Y;</span></div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = n-1; k &gt;= 0; k--) </div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;          {</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = k+1; i &lt; n; i++) </div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;               x[k] -= x[i]*L_[i][k];</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;         x[k] /= L_[k][k];</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;      }</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;        <span class="keywordflow">return</span> x;</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;}</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> Real&gt;</div>
<div class="line"><a name="l00188"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_cholesky.html#a8a3c0067663955146713a9aa3b8a3413">  188</a></span>&#160;<a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> <a class="code" href="class_j_a_m_a_1_1_cholesky.html#af0f727e2b0e989f7606cdb49de69f119">Cholesky&lt;Real&gt;::solve</a>(<span class="keyword">const</span> <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> &amp;B)</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;{</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;        <span class="keywordtype">int</span> n = L_.<a class="code" href="class_t_n_t_1_1_array1_d.html#ad0e3ae296c57454d4244f44076cd1e02">dim1</a>();</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;        <span class="keywordflow">if</span> (B.<a class="code" href="class_t_n_t_1_1_array2_d.html#a3997cd7973cd903cc46c0bd7abde03c0">dim1</a>() != n)</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;                <span class="keywordflow">return</span> <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a>();</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;        <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> X = B.<a class="code" href="class_t_n_t_1_1_array2_d.html#a475f33af47a33135fde05d1e01fdf0c3">copy</a>();</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;        <span class="keywordtype">int</span> nx = B.<a class="code" href="class_t_n_t_1_1_array2_d.html#a6efd5ac98f02bb42340be1d5cbf4c9c1">dim2</a>();</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;<span class="comment">// Cleve&#39;s original code</span></div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;<span class="preprocessor">#if 0</span></div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;<span class="preprocessor"></span>      <span class="comment">// Solve L*Y = B;</span></div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; n; k++) {</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = k+1; i &lt; n; i++) {</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; nx; j++) {</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;               X[i][j] -= X[k][j]*L_[k][i];</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;            }</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;         }</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; nx; j++) {</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;            X[k][j] /= L_[k][k];</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;         }</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;      }</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;      <span class="comment">// Solve L&#39;*X = Y;</span></div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = n-1; k &gt;= 0; k--) {</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; nx; j++) {</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;            X[k][j] /= L_[k][k];</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;         }</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; k; i++) {</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; nx; j++) {</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;               X[i][j] -= X[k][j]*L_[k][i];</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;            }</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;         }</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;      }</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;      <span class="comment">// Solve L*y = b;</span></div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;          <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j=0; j&lt; nx; j++)</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;          {</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; n; k++) </div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;                {</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;                        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; k; i++) </div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;               X[k][j] -= X[i][j]*L_[k][i];</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;                    X[k][j] /= L_[k][k];</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;                 }</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;      }</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;      <span class="comment">// Solve L&#39;*X = Y;</span></div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;     <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j=0; j&lt;nx; j++)</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;         {</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = n-1; k &gt;= 0; k--) </div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;                {</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;                <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = k+1; i &lt; n; i++) </div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;               X[k][j] -= X[i][j]*L_[i][k];</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;                X[k][j] /= L_[k][k];</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;                }</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;      }</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;        <span class="keywordflow">return</span> X;</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;}</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;}</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;<span class="comment">// namespace JAMA</span></div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;<span class="preprocessor"></span><span class="comment">// JAMA_CHOLESKY_H</span></div>
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